On recognition of strong graph bundles
Janez Žerovnik (2000)
Mathematica Slovaca
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Janez Žerovnik (2000)
Mathematica Slovaca
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Steven D. Noble, Dominic J. A. Welsh (1999)
Annales de l'institut Fourier
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Motivated by the work of Chmutov, Duzhin and Lando on Vassiliev invariants, we define a polynomial on weighted graphs which contains as specialisations the weighted chromatic invariants but also contains many other classical invariants including the Tutte and matching polynomials. It also gives the symmetric function generalisation of the chromatic polynomial introduced by Stanley. We study its complexity and prove hardness results for very restricted classes of graphs.
Zaslavsky, Thomas (1998)
The Electronic Journal of Combinatorics [electronic only]
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Alain Guénoche (2009)
RAIRO - Operations Research
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We first describe four recent methods to cluster vertices of an undirected non weighted connected graph. They are all based on very different principles. The fifth is a combination of classical ideas in optimization applied to graph partitioning. We compare these methods according to their ability to recover classes initially introduced in random graphs with more edges within the classes than between them.
Manju K. Menon, A. Vijayakumar (2010)
Discussiones Mathematicae Graph Theory
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The edge C₄ graph of a graph G, E₄(G) is a graph whose vertices are the edges of G and two vertices in E₄(G) are adjacent if the corresponding edges in G are either incident or are opposite edges of some C₄. In this paper, we show that there exist infinitely many pairs of non isomorphic graphs whose edge C₄ graphs are isomorphic. We study the relationship between the diameter, radius and domination number of G and those of E₄(G). It is shown that for any graph G without isolated vertices,...
Hoffmann, Michael, Matoušek, Jiří, Okamoto, Yoshio, Zumstein, Philipp (2011)
The Electronic Journal of Combinatorics [electronic only]
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Djidjev, Hristo N., Vrt'o, Imrich (2003)
Journal of Graph Algorithms and Applications
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